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Fishery Bulletin 88(3). 1990 



month, 45-70 mm at 2 months, 70-100 mm at 3 

 months, and 95-125 mm at 4 months, depending upon 

 cohort. These sizes were reasonable because growth 

 averaged 28-32 mm/30 days at 3-6 months of age in 

 May-July (Dentzau 1985). 



Apparent duration of the overall spawning period 

 was approximated following Geoghegan and Chit- 

 tenden (1982), as 



Time-specific mean size range early in life 

 Mean growth/day early in life 



Calculations were based on fish collected early in life, 

 i.e.. May- June; too few were collected before then (1-4 

 fish/cruise in March and April) to estimate growth. For 

 the numerator, time-specific size range was estimated 

 for each cohort as the mean of the 99% confidence in- 

 tervals for observations in that period. For the denom- 

 inator, individual growth increments were estimated 

 as the difference between (1) observed mean total 

 lengths on successive dates and (2) total lengths on suc- 

 cessive dates predicted from regressions. Individual 

 estimates of growth/day were then made as the in- 

 dividual growth increment divided by the time between 

 collection dates. Mean growth/day early in life was then 

 estimated as the average of individual growth/day 

 values between successive collections during May- 

 June. Dentzau (1985, table 3) details these calculations. 

 Calculations were also made using 90% confidence in- 

 tervals to compare how much successful spawning oc- 

 curred in a period shorter than the overall period. 



Hatching dates used to approximate time scales to 

 calculate growth were determined by a one-step itera- 

 tion process following Standard and Chittenden (1984). 

 An initial hatching date of 1 February was used to start 

 the approximation, because fish 50-90 mm, assumed 

 to be 2-3 months old, first appeared in March-April. 

 Quadratic regressions of total length on age in days 

 after 1 February were then used as models to estimate 

 an initial .r-intercept for each cohort; linear regression 

 was used if the quadratic term was not significant at 

 a = 0.05. Final hatching dates were calculated by using 

 the ir-intercept for each cohort to readjust the initial 

 .r-variable (time) scale, so each final growth curve 

 passed through the origin (Fig. 2). 



Recruitment patterns and movements in the Gulf 

 were determined by analyzing length frequencies and 

 catch-per-unit-effort against depth at specified "sea- 

 sons" (months) of the year; length-frequency data from 

 Galveston Bay, Texas (Gallaway and Strawn 1974), ex- 

 tended our analyses to estuaries. We use the words 

 "recruit" and "recruitment" in two ways: (1) to de- 

 scribe movement to areas by young P. octonemus 

 descending to the bottom from their pelagic early 

 stages, and (2) horizontal movements from estuaries 



Figure 3 



Length frequencies and cumulative percentage of all Polydnctyhis 

 octom-Tnus collected off Freeport, Texas, October 1977- August 1981. 



to the Gulf, or within the Gulf, by fishes already in the 

 exploited phase. The former conforms to Beverton and 

 Holt's (1957) meaning of recruitment (t^), because 

 these areas are generally exploited, and to Beverton 

 and Holt's (1957) and Ricker's (1975) meaning (t,), be- 

 cause fish also then enter the exploited phase of life. 

 Some gear selection for older, larger fish may occur 

 as part of these processes. 



Typical maximum life span was approximated by the 

 Beverton-Holt model parameter //^ (Gulland 1969), and 

 typical maximum size was approximated as a cor- 

 responding length (//J following the definition that 

 only 0.5-1.0% of the catch exceeds age t^ (Alverson 

 and Carney 1975, DeVries and Chittenden 1982). 

 Values of l^ were calculated from the cumulative fre- 

 quency for all fish captured (Fig. 3). Specific values of 

 ti were calculated from li by solving for time in von 

 Bertalanffy (Gulland 1969) and regression growth 

 equations (Fig. 2). 



Time and cohort-specific total annual mortality rates 

 (1 - S) were calculated using S = N/INo, where S = 

 rate of survival, and A'', and N,t are the numbers of fish 

 at age each month or per tow. Observed estimates were 

 compared against theoretical values calculated from 

 the expression Z = 4.6/number of years in life span 

 (Royce 1972:238). Total mortality rates, typical max- 

 imum life spans, maximum sizes, sizes at age, spawn- 

 ing period durations, and von Bertalanffy parameters 



